## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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2x } of T and otherwise let E ( d ) be the sum of all the projections E ( 2 ) for which lied , then the function E is a ... appearing in ( vi ) and to define the algebra of scalar

2x } of T and otherwise let E ( d ) be the sum of all the projections E ( 2 ) for which lied , then the function E is a ... appearing in ( vi ) and to define the algebra of scalar

**functions f**to which the formula may be applied .Page 986

This shows that I2 L and completes the proof of the lemma . Q.E.D. 7 THEOREM . ( Wiener Ly - closure theorem ) . Linear combinations of the translates of a

This shows that I2 L and completes the proof of the lemma . Q.E.D. 7 THEOREM . ( Wiener Ly - closure theorem ) . Linear combinations of the translates of a

**function f**in L ( R ) are dense in L ( R ) if and only if its transform f does ...Page 1075

14 Show that there exists continuous

14 Show that there exists continuous

**function f**in L ( -00 , +00 ) L ( -0 , +00 ) such that the limit in Exercise 12 fails to exist for x = 0 . 15 Show that there exists a**function f**in Lil - 00 , + ) for which the family of functions a ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### Common terms and phrases

additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero